Question

PHI, 8. Дано вектори ā(0; -3) i b(1; -1). Знайдіть кут між векторами ã i b.​

Answer 1

Ответ:

$| \overrightarrow{a}| = \sqrt{ {x}^{2} + {y}^{2} + {z}^{2} }$

$\overrightarrow{a}\overrightarrow{b} = x_{a} \times x_{y} + y_{a} \times y_{b} + z_{a} \times z_{b}$

$\displaystyle \cos( \alpha ) = \frac{\overrightarrow{a}\overrightarrow{b}}{ |\overrightarrow{a}| \times |\overrightarrow{b}| }$

$| \overrightarrow{a}| = \sqrt{ {0}^{2} + {( - 3) }^{2} } = 3$

$|\overrightarrow{b}| = \sqrt{ {1}^{2} + {( - 1)}^{2} } = \sqrt{1 + 1} = \sqrt{2}$

$\overrightarrow{a}\overrightarrow{b} = 0 \times 1 + ( - 3) \times ( - 1) = 3$

$\cos( \alpha ) = \frac{3}{3 \sqrt{2} } = \frac{1}{ \sqrt{2} } = \frac{ \sqrt{2} }{2}$

$\alpha = \arccos( \frac{ \sqrt{2} }{2} ) = {45}^{ \circ}$

α=45°